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The decay $B_c^+to J/psi K^+$ is observed for the first time using a data sample, corresponding to an integrated luminosity of 1.0 ${,fb}^{-1}$, collected by the LHCb experiment in $pp$ collisions at a centre-of-mass energy of $7mathrm{,Tekern -0.1em V}$. A yield of $46pm12$ events is reported, with a significance of 5.0 standard deviations. The ratio of the branching fraction of $B_c^+to J/psi K^+$ to that of $B_c^+to J/psipi^+$ is measured to be $0.069pm0.019pm0.005$, where the first uncertainty is statistical and the second is systematic.
We indicated in our previous work that for QED the role of the scalar potential which appears at the loop level is much smaller than that of the vector potential and in fact negligible. But the situation is different for QCD, one reason is that the l oop effects are more significant because $alpha_s$ is much larger than $alpha$, and secondly the non-perturbative QCD effects may induce a sizable scalar potential. In this work, we phenomenologically study the contribution of the scalar potential to the spectra of charmonia, bottomonia and $bbar c(bar b c)$ family. Taking into account both vector and scalar potentials, by fitting the well measured charmonia and bottomonia spectra, we re-fix the relevant parameters and test them by calculating other states of not only the charmonia, bottomonia, but also further the $bbar c$ family. We also consider the Lamb shift of the spectra.
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